相关论文: On Frink's type metrization of weighted graphs

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…

We develop a rigidity theory for bar-joint frameworks in Euclidean $d$-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class.…

The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…

We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means…

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…

Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…

We introduce a framework for network analysis based on random walks on directed acyclic graphs where the probability of passing through a given node is the key ingredient. We illustrate its use in evaluating the mutual influence of nodes…

Let $G_n$ be a random geometric graph with vertex set $[n]$ based on $n$ i.i.d.\ random vectors $X_1,\ldots,X_n$ drawn from an unknown density $f$ on $\R^d$. An edge $(i,j)$ is present when $\|X_i -X_j\| \le r_n$, for a given threshold…

We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport…

The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…

We prove a version of Clifford's theorem for metrized complexes. Namely, a metrized complex that carries a divisor of degree $2r$ and rank $r$ (for $0<r<g-1$) also carries a divisor of degree $2$ and rank $1$. We provide a structure theorem…

Let $G=(V,E)$ be a connected graph, let $v\in V$ be a vertex and let $e=uw\in E$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by $d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A vertex $w\in V$ distinguishes two edges…

In the theory of line graphs of undirected graphs there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, the exists no analogous…

Understanding causal relationships among the variables of a system is paramount to explain and control its behavior. For many real-world systems, however, the true causal graph is not readily available and one must resort to predictions…

Given a graph $G = (V,E)$ with vertex weights $w(v)$ and a desired number of parts $k$, the goal in graph partitioning problems is to partition the vertex set V into parts $V_1,\ldots,V_k$. Metrics for compactness, contiguity, and balance…

We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…

We prove that the edge-end space of an infinite graph is metrizable if and only if it is first-countable. This strengthens a recent result by Aurichi, Magalhaes Jr.\ and Real (2024). Our central graph-theoretic tool is the use of tree-cut…

Understanding network structure and having access to realistic graphs plays a central role in computer and social networks research. In this paper, we propose a complete, and practical methodology for generating graphs that resemble a real…

We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck…

For a fixed number of colors, we show that, in node-weighted split graphs, cographs, and graphs of bounded tree-width, one can determine in polynomial time whether a proper list-coloring of the vertices of a graph such that the total weight…